O 1mTwo sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6cm anddiffering with their phase constant, are travelling to the right with same velocity v= 60 m/s. The resultant wave function y res (x,t) will have the form:%3DO y_res (x,t) = 12(cm) cos(p/2) sin(150tx-3rt+p/2).O y_res (x,t) = 12(cm) cos(p/2) sin(3TX+150rt+9/2).%3DO y_res (x,t) = 12(cm) cos(p/2) sin(150rtx+3tt+p/2).O y-res (x,t) = 12(cm) cos(p/2) sin(3Ttx-150rt+q/2).O y_res (x,t) = 12(cm) cos(p/2) sin(3Ttx-180Ttt=p/2).%3DTwo sinusoidal waves travelling in the same direction with the same amplitude. O 4 loopsTwo transverse sinusoidal waves combining in a string are described by the wavefunctions y1= 0.02 sin(4tx+rtt) and y2 = 0.02 sin(4Ttx-Tt), where x and y are in%3Dmeters, and t is in seconds. If after superposition, a standing wave of 3 loops isformed, then the length of the string is:2 m1.5 m0.5 m0.75 m1 m

NOTE: As per guidelines, I can solve first question only. If you need help with other question, then…

Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 60 m/s. The resultant wave function y_res (x,t) will have the form: %3D

Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 60 m/s. The resultant wave function y_res (x,t) will have the form: %3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

The resultant intensity due to the constructive interference of two waves is 196 W/m2 . Evaluate the amplitude of each wave if the ratio of their amplitudes is 2/5
The resultant intensity due to the destructive interference of two waves is 36 W/m2. Evaluate the amplitude of each wave if the ratio of their amplitudes is 5/2
When a plane wave travels in a medium, the displace- ments of particles are given by y = 0.01 sin [27 (2t – 0.01x)] where x and y are in metre and t in second. Find (a) the amplitude, wavelength, wave velocity and frequency of the wave, (b) the phase difference between two positions of the same particle in a time interval of 0.25s and (c) the phase difference at a given instant of time between two particles 50 m apart.
%90 0 4G VeWIF Two sinusoidal waves of wavelength A = 2/3 m and amplitude A =6 cm and %3D differing with their phase constant, are travelling to the left with same velocity v = 50 m/s. The resultant %3D wave function y_res (x,t) will have the form: y_res (x,t) = 12(cm) cos(p/2) sin(150tx-3nt+p/2). y_res (x,t) = 12(cm) cos(p/2) sin(3rx-180rnt+p/2). %3D y_res (x,t) = 12(cm) cos(9/2) sin (3πx+150 πt+φ/2). y_res (x,t) = 12(cm) cos(p/2) sin(3tx-150rt+p/2). y_res (x,t) = 12(cm) cos(p/2) sin(150Ttx+3nt+p/2). %3D
The intensity I of a progressive wave is related to pressure amplitude P by I where Z is the acoustic impedance of a ultrasound wave in medium. Prove that 4Z₁Z2 the intensity transmission coefficient is T₁ = given that the intensity (Z₁ + Z₂)² = reflection coefficient is R, Z₁-Z₂ (Z₁ + Z₂)²*
Consider a monochromatic green lightwave with wavelength λ = 550 nm (1 nm = 1 * 10-9m). Assuming the speed of light in vacuum (which is close to the one in air) to be c = 3 * 108m/s, then: A. Calculate the period τ and the optical frequency v for green light? B. Write a sinusoidal harmonic wave with unit amplitude propagating towards the negative x-axis. Consider that for x = 0 and t = 0, the (initial) phase is (π/2). C. Plot the wave profile against x for following times: t = 0, 0.25τ, 0.5τ, and 0.75τ. Assume an arbitrary unit for the y-axis.
Simple hormic motion
Problem 2Given: A wave of 0.3 m wave height and period 1.3 seconds is generated in a wave tank. The wave tank is 90 m. long, 3 m wide, and 3 m deep and filled with fresh water to a depth of 1.5 m. The density of water is 997 kg/m3.Evaluate the water particle velocity and acceleration at the crest of the wave at still water level (SWL).
Two sinusoidal waves of wavelength A = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 60 m/s. The resultant wave function y_res (xt) will have the form: y_res (x,t) = 12(cm) cos(4/2) sin(3rtx-180nt+p/2). O y_res (x,t) = 12(cm) cos(9/2) sin(3rx-150nt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(150rtx-3nt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(150rx+3nt+p/2). O y_res (x,t) = 12(cm) cos(p/2) sin(3rx+150nt+p/2).
Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.
Two harmonic waves are given by: y1=Acos(kx−ωt) and y2=Asin(kx−wt+π/3) where k=5πm−1, ω=800πs−1 and A=4.0cm sin(theta1) +/- sin(theta2) = 2sin( (theta1 +/- theta2) /2) cos( (theta1 -/+ theta2) /2) Using the provided identity, find the equation of the resultant wave and its amplitude. Show all work.
Two progressive cosine waves y1(x, t) and y2(x, t) ( of type y(x, t) = Acos (kx ± ωt + φ) ) have the same amplitude A = 3.0cm, propagate in opposite directions, have the same wavelength λ = 1.5cm, the same propagation speed v = 15, 0cm/s, and they have a phase difference between them equal φ = +π/2 radians. Get the resulting waveform expression yR(x, t) of these two oscillatory motions. Show that it can be written as yR(x, t) = 6 cos (4, 19x +π/4) cos (62, 8t +π/4)